An admissibility condition in the class of unbiased estimators of finite population parameters

Summary A general sufficient condition is found for estimators of a finite population parameter to be admissible in the class of its unbiased estimators. The solution extends a result given by Godambe and Joshi and appears as a unified condition which applies indistinctly to those unbiased estimators of the most usual parameters (linear and quadratic forms of the population values) for which the previous admissibility proofs were worked out separately. A further more restrictive condition proves the admissibility of estimators concerning some parameters which are non polinominal functions of the population values.     

A robust biplot

This paper introduces a robust biplot which is related to multivariate M-estimates. The n × p data matrix is first considered as a sample of size n from some p-variate population, and robust M-estimates of the population location vector and scatter matrix are calculated. In the construction of the biplot, each row of the data matrix is assigned a weight determined in the preliminary robust estimation. In a robust biplot, one can plot the variables in order to represent characteristics of the robust variance-covariance matrix: the length of the vector representing a variable is proportional to its robust standard deviation, while the cosine of the angle between two variables is approximately equal to their robust correlation. The proposed biplot also permits a meaningful representation of the variables in a robust principal-component analysis. The discrepancies between least-squares and robust biplots are illustrated in an example.     

Constructing an unbiased estimator of population mean in finite populations using auxiliary information

The objective of this paper is to construct an unbiased estimator (up to order 0(1/n)) of the population mean of the study variatey which is more efficient than the sample mean of the ‘n’ obsrvedy-values. In particular, the unbiased estimators are discussed for the cases of positive and negative correlations of the study variatey and the auxiliary variatex.     

Alternative mean-squared error estimators for synthetic estimators of domain means

In forest management surveys, the mean of a variable of interest (Y) in a population composed of N equal area spatial compact elements is increasingly estimated from a model linking Y to an auxiliary vector X known for all elements in the population. It is also desired to have synthetic estimates of the mean of Y in spatially compact domains (forest stands) with no or at most one sample-based observation of Y. We develop three alternative estimators of mean-squared errors (MSE) that reduce the risk of a serious underestimation of the uncertainty in a synthetic estimate of a domain mean in cases where the employed model does not accounts for domain effects nor spatial autocorrelation in unobserved residual errors. Expansions of the estimators including anticipated effects of a spatial autocorrelation in residual errors are also provided. Simulation results indicate that the conventional model-dependent (MD) population-level estimator of variance in a synthetic estimate of a domain mean underestimates uncertainty by a wide margin. Our alternative estimators mitigated, in settings with weak to moderate domain effects and relatively small sample sizes, to a large extent, the problem of underestimating uncertainty. We demonstrate applications with examples from two actual forest inventories.     

New influence diagnostics in ridge regression

We occasionally find that a small subset of the data exerts a disproportionate influence on the fitted regression model. We would like to locate these influential points and assess their impact on the model. However, the existence of influential data is complicated by the presence of collinearity (see, e.g. [15 E. Walker and J. Birch, Influence measures in ridge regression, Technometrics 30 (1989), pp. 221–227. doi: 10.1080/00401706.1988.10488370[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]). In this article we develop a new influence statistic for one or a set of observations in linear regression dealing with collinearity. We show that this statistic has asymptotically normal distribution and is able to detect a subset of high ridge leverage outliers. Using this influence statistic we also show that when ridge regression is used to mitigate the effects of collinearity, the influence of some observations can be drastically modified. As an illustrative example, simulation studies and a real data set are analysed.     

组合预测贝叶斯模型研究

评述了组合预测的基本思想和组合预测贝叶斯模型的研究现状,研究了多步贝叶斯信息更新情况下针对不同偏性特征的无偏组合预测模型,讨论了结合非样本信息和样本信息的组合权重贝叶斯更新模型,扩展了贝叶斯组合预测模型的现有成果,指出了进一步研究的方向．     

The returns to continuous training in Germany: new evidence from propensity score matching estimators

The present paper examines the wage effects of continuous training programs using individual-level data from the German Socio Economic Panel (GSOEP). In order to account for selectivity in training participation we estimate average treatment effects (ATE and ATT) of general and firm-specific continuous training programs using several state-of-the-art propensity score matching (PSM) estimators. Additionally, we also apply a combined matching difference-in-differences (MDiD) estimator to account for unobserved individual characteristics (e.g. motivation, ability). While the estimated ATE and ATT for general training are significant ranging between about 4 and 7.5%, the corresponding wage effects of firm-specific training are mostly insignificant. Using the more appropriate MDiD estimator, however, we find a more precise and highly significant wage effect of about 5–6%, though only for general training and not for firm-specific training. These results are consistent with standard human capital theory insofar as general training is associated with larger wage increases than firm-specific training. Furthermore, we conclude that firms may intend to use specific training to adjust to new job requirements, while career-relevant changes may be conditioned to general training.

Small area estimation of expenditure means and ratios under a unit-level bivariate linear mixed model

Under a unit-level bivariate linear mixed model, this paper introduces small area predictors of expenditure means and ratios, and derives approximations and estimators of the corresponding mean squared errors. For the considered model, the REML estimation method is implemented. Several simulation experiments, designed to analyze the behavior of the introduced fitting algorithm, predictors and mean squared error estimators, are carried out. An application to real data from the Spanish household budget survey illustrates the behavior of the proposed statistical methodology. The target is the estimation of means of food and non-food household annual expenditures and of ratios of food household expenditures by Spanish provinces.     

New modified moment estimators for the two-parameter weighted Lindley distribution

We propose a modification of the moment estimators for the two-parameter weighted Lindley distribution. The modification replaces the second sample moment (or equivalently the sample variance) by a certain sample average which is bounded on the unit interval for all values in the sample space. In this method, the estimates always exist uniquely over the entire parameter space and have consistency and asymptotic normality over the entire parameter space. The bias and mean squared error of the estimators are also examined by means of a Monte Carlo simulation study, and the empirical results show the small-sample superiority in addition to the desirable large sample properties. Monte Carlo simulation study showed that the proposed modified moment estimators have smaller biases and smaller mean-square errors than the existing moment estimators and are compared favourably with the maximum likelihood estimators in terms of bias and mean-square error. Three illustrative examples are finally presented.     

On the weighted mixed Liu-type estimator under unbiased stochastic restrictions

In this article, we introduce the weighted mixed Liu-type estimator (WMLTE) based on the weighted mixed and Liu-type estimator (LTE) in linear regression model. We will also present necessary and sufficient conditions for superiority of the weighted mixed Liu-type estimator over the weighted mixed estimator (WME) and Liu type estimator (LTE) in terms of mean square error matrix (MSEM) criterion. Finally, a numerical example and a Monte Carlo simulation is also given to show the theoretical results.